Question

4=log[7]2401

Answer 1

[AI-generated answer — Explain Bot]

To solve the equation 4 = log[7]2401, we need to understand logarithms and how they relate to exponentiation.

In general, a logarithm is the inverse operation of exponentiation. It tells us what exponent we need to raise a base to in order to get a certain value. In this equation, the base is 7, and we need to find the exponent that gives us 2401.

To solve the equation, we can rewrite it by exponentiating both sides with base 7. Remember that when we exponentiate both sides of an equation, we use the same base on both sides:

7^4 = 7^(log[7]2401)

On the left-hand side, we have 7 raised to the power of 4. This simplifies to 2401:

2401 = 7^(log[7]2401)

Now, we have an equation without any logarithms. We know that if two exponential expressions have the same base, then their exponents must be equal. So we can set the exponents equal to each other:

log[7]2401 = 4

Therefore, the value of log[7]2401 is equal to 4.